How do I Delete geometry? Separate objects are one piece?
If you want to have the objects separated go to edit mode instead of object mode, then select one mesh pressing "L" while your mouse is over the mesh you want to select, then press "P" to separate the selected mesh into a new object.

When you're in edit mode it doesn´t matter if you add a new cube or cilinder it will be part of the same object you were editing on first place.